Apple’s iPhone is getting more appealing to business users, but BlackBerry maker RIM says it will prevail among the corporate set.

Research in Motion co-CEO Jim Balsillie

For an executive on the go, there’s no better device for powering through e-mail than a BlackBerry, the No. 1 smartphone in North America. But increasingly businesspeople also want cool downloadable software, or apps, popularized by Apple’s iPhone. Can BlackBerry, with a paltry 6,500 available apps — compared with Apple’s 185,000 and Google (GOOG) Android’s 38,000 — maintain its lead among corporate users?

Research in Motion, the maker of BlackBerry devices and software, contends that there’s more to a great smartphone than standalone apps, and indeed, BlackBerry loyalists (and their tech departments) say the security and usability of the RIM gadgets trump the features of more app-centric phones. “I’m a BlackBerry devotee,” says Zach Nelson, CEO of NetSuite. “Sure, I have a Droid and an iPhone, and they’re fine for surfing the web. The BlackBerry is an e-mail machine. It’s designed for a purpose.”

RIM (RIMM) co-CEO Jim Balsillie says he has “never felt more confident about the opportunities” for the company. RIM had a record fiscal 2009 in which revenue grew 35%, to $15 billion. The company shipped 37 million phones last year, up 42% from the previous year, and international users, once a fraction of customers, accounted for 48% of sales in the most recent quarter.

Balsillie says RIM is taking steps to make BlackBerrys more fun and functional. A raft of cool new versions of the phone (probably including some touchscreen models) will be unveiled later this year, and Balsillie promises a much better web-surfing experience — RIM recently acquired Torch Mobile, maker of the popular WebKit-based mobile browser — that could lead to a rise in web-based applications such as a version of LinkedIn that integrates a handset’s contact list. RIM calls these “super apps.”

Meanwhile, RIM continues to court developers for its app storefront, known as BlackBerry App World. The company, based in Waterloo, Ontario, holds annual Silicon Valley conferences for software makers and offers them technical support and marketing advice. But some app makers complain that RIM’s tools are clumsy, and Forrester Research analyst Charles Golvin thinks the entire RIM software platform needs to be overhauled. “Developers have to do a lot of work,” he says, to make sure an app works, and even when it does, only one model, the Black- Berry Storm, boasts a touchscreen that makes so many Apple (AAPL) and Android apps come to life.

A paucity of apps may not be a problem for BlackBerry today — analysts predict RIM will grow its top line by 29% in fiscal 2010 — but the company can’t neglect downloadable apps forever. While chieftains such as NetSuite’s Nelson swear by their BlackBerrys, a new generation of executives wants the coolest-looking device with the freshest new software — and apps. If enough corporate types want app-friendly phones, RIM’s most-favored-device status in corporations could be threatened.